ENEN90028 Chap.4 Sampling Units, Estimates and Data Types
Sampling Units, Estimates and Data Types
The sampling unit is the level at which an impact comparison is replicated. Samples and sub-samples characterise that unit but do not create additional treatment replication. This chapter joins the hierarchy to quantitative summaries: mean, sample standard deviation and standard error, plus continuous, count, ordinal and categorical data types that constrain analysis and graphics.
What this chapter covers
- 01
Sampling units as independent replicates
- 02
Samples and nested sub-samples
- 03
Mean and sample standard deviation
- 04
Standard error and independent sample size
- 05
Accuracy versus precision
- 06
Continuous count ordinal and categorical data
Worked example · free
Compute oxygen mean and standard error
- 1The mean is 26.4 divided by 4, which equals 6.60 mg/L.
- 1The squared deviations sum to 0.40.
- 1Sample standard deviation is the square root of 0.40 divided by 3, which equals 0.365 mg/L.
- 1Standard error is 0.365 divided by 2, which equals 0.183 mg/L.
Key terms
- Sampling unit
- The independent unit at which an impact is tested.
- Sample
- One or more measurements used to characterise a sampling unit.
- Sub-sample
- A nested observation that improves the estimate within a unit.
- Sample standard deviation
- A measure of spread among sample observations.
- Standard error
- A measure of uncertainty in the estimated mean.
- Ordinal data
- Ordered categories whose gaps are not assumed equal.
Sampling Units, Estimates and Data Types FAQ
Why are sub-samples not treatment replicates?
They share the same intervention history and environmental unit, so their errors may be correlated. Sub-samples improve the estimate of that unit, while independent sampling units reveal variation in the treatment contrast across places or times that genuinely received separate instances of the comparison.
What is the difference between standard deviation and standard error?
Sample standard deviation describes spread among observations. Standard error describes uncertainty in the estimated mean and is calculated by dividing the sample standard deviation by the square root of the independent sample size. A small standard error does not guarantee an unbiased measurement.
Why does data type matter?
Continuous, count, ordinal and categorical variables have different bounds and meanings. Their type affects appropriate summaries, plots and statistical models. Giving category labels numeric codes does not create equal intervals, while counts remain discrete and bounded at zero even when their average is fractional.
Assessment move
Draw the sampling hierarchy for every practice design and circle the level where the intervention differs. Recompute the mean, sample standard deviation and standard error for small datasets by hand. Label each variable with type, unit and sampling level before choosing a graph or test. When a question presents many rows, resist counting them until independence is established. Build a hierarchy diagram from the outside inward.
Write the sampling unit first, then place samples and sub-samples inside it. Add the intervention label only at the level where status changes. This visual makes it much harder to count quadrats, cores or repeated readings as treatment replicates. For numerical practice, use four or five observations so every step can be checked.
Calculate the mean, write each deviation, square the deviations, divide their sum by n minus one, take the square root and then divide by the square root of the independent n for standard error. Keep the unit beside every answer. After the calculation, write one interpretation: standard deviation describes spread among the observations, while standard error describes precision of the estimated mean.
Create counterexamples that expose the independence rule. Compare five dams measured once with one dam measured five times. Both produce five rows, but only the first design may provide five independent dam observations. Repeat the exercise with paddocks and soil cores, forest patches and quadrats, or field samples and instrument repeats. For data types, make four lists: continuous, count, ordinal and categorical.
Explain the feature that determines membership rather than relying on the way a spreadsheet stores the value. A low-medium-high code remains ordinal even if stored as 1, 2 and 3; bird abundance remains a count even when a model estimates a non-integer mean. Before selecting any analysis, annotate the variable type, measurement unit, independent unit and aggregation rule.
This small protocol connects the field design to the statistical method and protects against flattening nested data. Finish by explaining how greater within-unit sampling can improve precision without improving independent replication. That distinction is the central quantitative idea of the chapter and a frequent source of convincing but invalid analyses. Add a reconstruction drill using a mock spreadsheet.
From columns for site, plot, core, date and treatment, sketch the hierarchy and identify which repeated rows share a unit. Then state the independent n for the treatment contrast and the within-unit n used to estimate each site. If the identifiers cannot support that reconstruction, specify the field-record change needed before analysis.
For numerical answers, perform a reasonableness check: the mean should lie within the observed range, standard deviation cannot be negative, and standard error should use the independent sample count appropriate to the estimate. Compare two datasets with the same mean but different spread, then two designs with similar spread but different independent n. Explain which quantity changes and why.
This connects calculation mechanics to monitoring decisions about variability, precision and added replication rather than leaving the formulas isolated from design.
